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// Copyright (c) 1999,2007 // Utrecht University (The Netherlands), // ETH Zurich (Switzerland), // INRIA Sophia-Antipolis (France), // Max-Planck-Institute Saarbruecken (Germany), // and Tel-Aviv University (Israel). All rights reserved. // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Number_types/include/CGAL/leda_integer.h $ // $Id: include/CGAL/leda_integer.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Andreas Fabri, Michael Hemmer #ifndef CGAL_LEDA_INTEGER_H #define CGAL_LEDA_INTEGER_H #include #include #include #include #include #include #include // for To_interval #include #include namespace CGAL { template <> class Algebraic_structure_traits< leda_integer > : public Algebraic_structure_traits_base< leda_integer, Euclidean_ring_tag > { public: typedef Tag_true Is_exact; typedef Tag_false Is_numerical_sensitive; typedef INTERN_AST::Is_square_per_sqrt< Type > Is_square; class Gcd : public CGAL::cpp98::binary_function< Type, Type, Type > { public: Type operator()( const Type& x, const Type& y ) const { // By definition gcd(0,0) == 0 if( x == Type(0) && y == Type(0) ) return Type(0); return CGAL_LEDA_SCOPE::gcd( x, y ); } CGAL_IMPLICIT_INTEROPERABLE_BINARY_OPERATOR( Type ) }; // Unfortunately the behavior of leda has changed here several times // The following Div_mod is invariant under these changes // However, the Div and Mod defined below might be more efficient // TODO: recover Div Mod implementation for all leda versions class Div_mod { public: typedef Type first_argument_type; typedef Type second_argument_type; typedef Type& third_argument_type; typedef Type& fourth_argument_type; typedef void result_type; void operator()(const Type& x, const Type& y, Type& q, Type& r) const { q = x / y; r = x - q*y; CGAL_postcondition(x == y*q + r); if (r == 0) return; // round q towards zero if ( r.sign() != x.sign() ){ q -= x.sign(); r -= x.sign()*y; } CGAL_postcondition(x == y*q + r); CGAL_postcondition(r.sign() == x.sign()); } }; // Div defined via base using Div_mod // Mod defined via base using Div_mod // This code results in an inconsistent div/mod for some leda versions // TODO: reactivate this code // typedef INTERN_AST::Div_per_operator< Type > Div; // class Mod // : public CGAL::cpp98::binary_function< Type, Type, // Type > { // public: // Type operator()( const Type& x, const Type& y ) const { // Type m = x % y; // return m; // } // CGAL_IMPLICIT_INTEROPERABLE_BINARY_OPERATOR( Type ) // }; class Sqrt : public CGAL::cpp98::unary_function< Type, Type > { public: Type operator()( const Type& x ) const { return CGAL_LEDA_SCOPE::sqrt( x ); } }; }; template <> class Real_embeddable_traits< leda_integer > : public INTERN_RET::Real_embeddable_traits_base< leda_integer , CGAL::Tag_true > { public: class Abs : public CGAL::cpp98::unary_function< Type, Type > { public: Type operator()( const Type& x ) const { return CGAL_LEDA_SCOPE::abs( x ); } }; class Sgn : public CGAL::cpp98::unary_function< Type, ::CGAL::Sign > { public: ::CGAL::Sign operator()( const Type& x ) const { return (::CGAL::Sign) CGAL_LEDA_SCOPE::sign( x ); } }; class Compare : public CGAL::cpp98::binary_function< Type, Type, Comparison_result > { public: Comparison_result operator()( const Type& x, const Type& y ) const { return (Comparison_result) CGAL_LEDA_SCOPE::compare( x, y ); } }; class To_double : public CGAL::cpp98::unary_function< Type, double > { public: double operator()( const Type& x ) const { return x.to_double(); } }; class To_interval : public CGAL::cpp98::unary_function< Type, std::pair< double, double > > { public: std::pair operator()( const Type& x ) const { leda::bigfloat h(x); double abs_err = 0; double low =h.to_double(abs_err, leda::TO_N_INF); double high =h.to_double(abs_err, leda::TO_P_INF); return std::make_pair(low,high); } }; }; template<> class Modular_traits< ::leda::integer > { typedef Residue MOD; public: typedef ::leda::integer NT; typedef ::CGAL::Tag_true Is_modularizable; typedef MOD Residue_type; struct Modular_image{ Residue_type operator()(const NT& a){ return Residue_type ((a%NT(MOD::get_current_prime())).to_long()); } }; struct Modular_image_representative{ NT operator()(const Residue_type& x){ return NT(x.get_value()); } }; }; // // Needs_parens_as_product // template <> struct Needs_parens_as_product { bool operator()(const leda_integer& x) { return CGAL_NTS is_negative(x); } }; // missing mixed operators inline bool operator==(int a, const leda_integer& b) { return b == a; } inline bool operator!=(int a, const leda_integer& b) { return b != a; } template <> struct Split_double { void operator()(double d, leda_integer &num, leda_integer &den) const { std::pair p = split_numerator_denominator(d); num = leda_integer(p.first); den = leda_integer(p.second); } }; // Benchmark_rep specialization template<> class Benchmark_rep< leda_integer > { const leda_integer& t; public: //! initialize with a const reference to \a t. Benchmark_rep( const leda_integer& tt) : t(tt) {} //! perform the output, calls \c operator\<\< by default. std::ostream& operator()( std::ostream& out) const { out << t; return out; } static std::string get_benchmark_name() { return "Integer"; } }; } //namespace CGAL // Unary + is missing for leda::integer namespace leda { inline integer operator+( const integer& i) { return i; } } // namespace leda //since types are included by LEDA_coercion_traits.h: #include #include #include #include #endif // CGAL_LEDA_INTEGER_H